{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1fc1999a-22ea-40ca-a6fa-0837d0e6513b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ffbc8ce7-ce53-4fd8-8e31-d00bf35a589e",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d3375f12-7797-4842-8393-fd3512249765",
   "metadata": {},
   "outputs": [],
   "source": [
    "X1 = 2*np.random.rand(100,1)\n",
    "X2 = 2*np.random.rand(100,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "69328953-b906-4f7f-9d3d-cf47ee4e14d4",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.74908024],\n",
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       "       [0.31198904],\n",
       "       [0.11616722],\n",
       "       [1.73235229],\n",
       "       [1.20223002],\n",
       "       [1.41614516],\n",
       "       [0.04116899],\n",
       "       [1.9398197 ],\n",
       "       [1.66488528],\n",
       "       [0.42467822],\n",
       "       [0.36364993],\n",
       "       [0.36680902],\n",
       "       [0.60848449],\n",
       "       [1.04951286],\n",
       "       [0.86389004],\n",
       "       [0.58245828],\n",
       "       [1.22370579],\n",
       "       [0.27898772],\n",
       "       [0.5842893 ],\n",
       "       [0.73272369],\n",
       "       [0.91213997],\n",
       "       [1.57035192],\n",
       "       [0.39934756],\n",
       "       [1.02846888],\n",
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       "       [1.2150897 ],\n",
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       "       [1.19579996],\n",
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       "       [0.176985  ],\n",
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       "       [1.65747502],\n",
       "       [0.71350665],\n",
       "       [0.56186902],\n",
       "       [1.08539217],\n",
       "       [0.28184845],\n",
       "       [1.60439396],\n",
       "       [0.14910129],\n",
       "       [1.97377387],\n",
       "       [1.54448954],\n",
       "       [0.39743136],\n",
       "       [0.01104423],\n",
       "       [1.63092286],\n",
       "       [1.41371469],\n",
       "       [1.45801434],\n",
       "       [1.54254069],\n",
       "       [0.1480893 ],\n",
       "       [0.71693146],\n",
       "       [0.23173812],\n",
       "       [1.72620685],\n",
       "       [1.24659625],\n",
       "       [0.66179605],\n",
       "       [0.1271167 ],\n",
       "       [0.62196464],\n",
       "       [0.65036664],\n",
       "       [1.45921236],\n",
       "       [1.27511494],\n",
       "       [1.77442549],\n",
       "       [0.94442985],\n",
       "       [0.23918849],\n",
       "       [1.42648957],\n",
       "       [1.5215701 ],\n",
       "       [1.1225544 ],\n",
       "       [1.54193436],\n",
       "       [0.98759119],\n",
       "       [1.04546566],\n",
       "       [0.85508204],\n",
       "       [0.05083825],\n",
       "       [0.21578285]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "63b3ae7e-b6e8-460d-a612-0f9c10357477",
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = 5 + 4*X1 + 3*X2 + np.random.randn(100,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "37c6e983-53c3-40bd-ae80-3c59dda4ba9d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7.50487134],\n",
       "       [16.65643062],\n",
       "       [13.03515989],\n",
       "       [12.1263406 ],\n",
       "       [13.55932248],\n",
       "       [ 8.21754246],\n",
       "       [ 6.73566294],\n",
       "       [17.11926961],\n",
       "       [10.20702742],\n",
       "       [11.91354469],\n",
       "       [ 8.06178025],\n",
       "       [12.90592422],\n",
       "       [18.20110317],\n",
       "       [11.96021609],\n",
       "       [11.07708244],\n",
       "       [13.5927926 ],\n",
       "       [12.01058229],\n",
       "       [ 9.56373564],\n",
       "       [12.92139971],\n",
       "       [ 9.75007629],\n",
       "       [14.66236238],\n",
       "       [11.83365066],\n",
       "       [ 9.52186884],\n",
       "       [ 9.41838954],\n",
       "       [10.02917274],\n",
       "       [15.2975885 ],\n",
       "       [11.24082202],\n",
       "       [16.99842817],\n",
       "       [10.40669668],\n",
       "       [ 7.57892956],\n",
       "       [11.29393234],\n",
       "       [ 8.17931227],\n",
       "       [ 6.01614216],\n",
       "       [15.33077582],\n",
       "       [18.85575211],\n",
       "       [13.33356746],\n",
       "       [ 9.70286017],\n",
       "       [ 8.48464344],\n",
       "       [12.20912687],\n",
       "       [15.20831124],\n",
       "       [11.96508339],\n",
       "       [ 9.22637028],\n",
       "       [ 8.43178013],\n",
       "       [14.46515046],\n",
       "       [ 7.89542538],\n",
       "       [10.67522506],\n",
       "       [11.20928333],\n",
       "       [11.03364801],\n",
       "       [10.0403421 ],\n",
       "       [ 8.71149896],\n",
       "       [19.28932358],\n",
       "       [13.69223598],\n",
       "       [12.0076914 ],\n",
       "       [14.15751033],\n",
       "       [16.21213782],\n",
       "       [14.34111146],\n",
       "       [10.25580099],\n",
       "       [14.99031208],\n",
       "       [ 7.35853409],\n",
       "       [13.10750638],\n",
       "       [11.27011888],\n",
       "       [11.61601849],\n",
       "       [15.11580909],\n",
       "       [11.82764394],\n",
       "       [ 7.01638948],\n",
       "       [14.11656503],\n",
       "       [ 7.56671064],\n",
       "       [12.61856105],\n",
       "       [ 8.15571457],\n",
       "       [14.57318796],\n",
       "       [15.92960452],\n",
       "       [ 5.07653655],\n",
       "       [ 7.64480342],\n",
       "       [13.97161668],\n",
       "       [14.59017551],\n",
       "       [10.80051114],\n",
       "       [14.60048549],\n",
       "       [ 8.59236704],\n",
       "       [12.75773913],\n",
       "       [ 6.96853673],\n",
       "       [13.99679735],\n",
       "       [10.01562579],\n",
       "       [15.33929   ],\n",
       "       [11.40642194],\n",
       "       [ 7.01036575],\n",
       "       [11.74782517],\n",
       "       [15.07839616],\n",
       "       [14.28409798],\n",
       "       [14.48308467],\n",
       "       [10.11409671],\n",
       "       [ 7.02035785],\n",
       "       [16.95500804],\n",
       "       [15.28849232],\n",
       "       [12.95432509],\n",
       "       [12.72697087],\n",
       "       [10.39229299],\n",
       "       [15.30305095],\n",
       "       [14.20797142],\n",
       "       [ 9.26498761],\n",
       "       [11.46024664]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ad5ab20b-236f-44a9-98f1-a72191a621e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100,1)),X1,X2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "14f97099-3ebe-4a40-a44e-e076abab8437",
   "metadata": {},
   "outputs": [],
   "source": [
    "θ = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fa8669bc-8eda-4339-bc75-a84c946c905e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.91061004],\n",
       "       [3.82913734],\n",
       "       [3.35965571]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "θ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a056b017-b1a1-4145-8e61-5a825f42ac6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_new = np.array([[0,0],[2,3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "dd788aaf-9996-4c66-b55c-4a3d4fb65fe8",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_new_b = np.c_[np.ones((2,1)),X_new]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "48695e35-1b64-4de6-97bc-faf4608e8ce1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0.]\n",
      " [1. 2. 3.]]\n"
     ]
    }
   ],
   "source": [
    "print(X_new_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4d27454e-1e0b-4bb5-b563-94239dd23cf6",
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_predict = X_new_b.dot(θ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2e46b11a-ea65-42a4-8b77-98f4ca5adb8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.91061004],\n",
       "       [22.64785183]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "bdef211c-a763-45ac-814f-500ba562a30b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 2]\n"
     ]
    }
   ],
   "source": [
    "print(X_new[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "31c1519b-8570-49ad-9622-481f11f5ac4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new[:,0],Y_predict,'r-')\n",
    "plt.plot(X1,Y,'b.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e2b29e05-b4bf-4c6a-b60e-1363f3fcfd20",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
